We study the optimal insurance design problem. This is a risk sharing problem between an insured and an insurer. The main novelty in this paper is that we study this optimization problem under a risk-adjusted premium calculation principle for the insurance cover. This risk-adjusted premium...

These notes are strongly motivated by practitioners who have been seeking for advise in stochastic claims reserving modeling under Solvency 2 and under the Swiss Solvency Test. There have been tremendous developments since the publication of our first book Stochastic Claims Reserving Methods in...

The aim of this contribution is to revisit, clarify and complete the picture of uncertainty estimates in the chain-ladder (CL) claims reserving method. Therefore, we consider the conditional mean square error of prediction (MSEP) of the total prediction uncertainty (using Mack's formula) and the...

We present a novel stochastic model for claims reserving that allows us to combine claims payments and incurred losses information. The main idea is to combine two claims reserving models (Hertig's (1985) model and Gogol's (1993) model ) leading to a log-normal paid-incurred chain (PIC) model....

We present the one-year claims development result (CDR) in the paid-incurred chain (PIC) reserving model. The PIC reserving model presented in Merz and Wüthrich (2010) is a Bayesian stochastic claims reserving model that considers simultaneously claims payments and incurred losses information...

Popular yield curve models include affine term structure models. These models are usually based on a fixed set of parameters which is calibrated to the actual financial market conditions. Under changing market conditions also parametrization changes. We discuss how parameters need to be updated...

Abstract For solvency purposes insurance companies need to calculate so-called best-estimate reserves for outstanding loss liability cash flows and a corresponding risk margin for non-hedgeable insurance-technical risks in these cash flows. In actuarial practice, the calculation of the risk...